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December 14, 2020 16:00–16:50, International webinar “Actual problems of the theory of algebraic groups”, online, December 14–16, 2020  


Root systems and root lattices in number fields

V. L. Popov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
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Abstract: The following construction of the root system of type $G_2$ is known (see the book by J.-P. Serre "Lie algebras and Lie groups", p. 315, Russian translation): “It can be described as a set algebraic integers of the cyclotomic field generated by the cube root of unity, with the norm 1 or 3". This talk, based on the joint results with Yu. G. Zarhin, is devoted to realization of root systems, their Weyl groups and their root lattices in the form of subsets, groups and lattices, naturally associated with fields of algebraic numbers.

Supplementary materials: slroots.pdf (903.4 Kb)
 
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